Answer:
[tex]\huge\boxed{3.873}[/tex]
Step-by-step explanation:
Note that the squares are on the sides of these triangles are on the hypotenuse/one leg.
We know that the area of a square is [tex]l^2[/tex] where l is the length. Since we know the area, we can find the square root of the area to find the side length.
So the side lengths are [tex]\sqrt{25}[/tex] and [tex]\sqrt{10}[/tex].
Since we know the hypotenuse is [tex]\sqrt{25}[/tex] and one of the legs is [tex]\sqrt{10}[/tex], we can use the Pythagorean Theorem to find the missing side.
The Pythagorean Theorem states that [tex]a^2 + b^2 = c^2[/tex], where c is the hypotenuse and a/b are the legs.
We know the hypotenuse and a leg, so we can substitute inside
[tex]a^2 + \sqrt{10}^2 = \sqrt{25}^2[/tex]
Squaring a square root is the same as doing nothing.
[tex]a^2 + 10 = 25\\\\a^2 = 25-10\\\\a^2 = 15\\\\a = \sqrt{15}\\\\a \approx 3.873[/tex]
Hope this helped!
